In drilling wells for oil and gas exploration, understanding the structure and properties of the associated geological formation provides information to aid such exploration. Measurements in a borehole are typically performed to attain this understanding. Induction tools can make accurate resistivity readings of formations downhole and are an important part of well-logging. The reading of these tools is based on the induction principle in which the transmitter produces a magnetic flux, which is picked up by the receiver.
Multi-coupling-component signals of electromagnetic (EM) resistivity logging tools are widely used to explore formation parameters, such as formation anisotropy, relative dip angle, boundaries, etc. Inversion processing of data to determine formation parameters can be performed according to a modeling approach for the formation. Inversion operations can include a comparison of measurements to predictions of a model such that a value or spatial variation of a physical property can be determined. In inversion, measured data may be applied to construct a model that is consistent with the data. For examining, an inversion operation can include determining a variation of electrical conductivity in a formation from measurements of induced electric and magnetic fields. Other techniques, such as a forward model, deal with calculating expected observed values with respect to an assumed model. In zero-dimensional (0D) inversion, there is no variation in the formation, such as in a homogenous formation. In one dimensional (1D) modeling, there is variation in one direction such as a formation of parallel layers. In two dimensional (2D) modeling, there is variation in two directions and, in three dimensional (3D) modeling, there is variation in three directions. In general, a coordinate system in which the above dimensions are defined can be Cartesian or cylindrical. In borehole applications, a cylindrical coordinate system is often used.
In general, zero-dimensional (0D) inversion adopting these coupling components is attractive owing to its simplicity and fast computation. Several processing schemes have been proposed on the basis of 0D inversion using various coupling components to calculate formation parameters. Based on distinct sensitivities of these coupling components, 0D inversion is able to provide accurate inverted formation model at arbitrary wellbore inclinations, especially while the EM tool is located in a thick bed. Processing schemes have provided successful determination of anisotropy parameters, which may include horizontal resistivity, vertical resistivity, relative dip angle, and relative strike, presented by both synthetic responses and field data. A synthetic response is a modeled response of a tool with respect to known parameters of the formation to which the tool is being applied. The synthetic response can be created by numerically modeling the interaction of the tool and the formation, usually involving simulation. In a synthetic log, the simulation may be conducted for each depth of the log on a point by point basis.
In a multi-component electromagnetic logging tool having three orthogonal transmitter coils (TX, TY, and TZ) and three orthogonal receiver coils (RX, RY, and RZ), the magnetic field H in the receiver coils can be represented in terms of the magnetic moments M at the transmitters and a coupling matrix C as:H=CM  (1)Equation (1) can be expressed as:
                              [                                                                      H                  x                                                                                                      H                  y                                                                                                      H                  z                                                              ]                =                              [                                                                                C                    xx                                                                                        C                    xy                                                                                        C                    xz                                                                                                                    C                    yx                                                                                        C                    yy                                                                                        C                    yz                                                                                                                    C                    zx                                                                                        C                    zy                                                                                        C                    zz                                                                        ]                    ⁡                      [                                                                                M                    x                                                                                                                    M                    y                                                                                                                    M                    z                                                                        ]                                              (        2        )            where MX, MY, and MZ are the magnetic moments of the transmitted signal emitted by transmitters TX, TY, and TZ, respectively. HX, HY, and HZ are the magnetic fields, which are proportional to the received signal at the receiver antennas RX, RY, and RZ, respectively. Nine absolute or differential measurements can be obtained when each antenna is fired and a signal is measured at each of the three receivers, respectively. Here differential means the complex ratio (or equivalently amplitude ratio or phase difference) between signals from two spatially separated receivers used in the place of one signal from one receiver. These nine measurements enable the determination of a complete coupling matrix C. The components, CIJ, can be defined as CIJ=aIJ·VIJ, where I is the index of receiver RX, RY, and RZ, J is the index of transmitter TX, TY, and TZ, aIJ is a constant coefficient determined by the tool design, and VIJ is a complex value representing the signal amplitude and phase shift measured by receiver I in response to the firing of transmitter J. The coupling matrix can be used to determine formation properties, for example, using an inversion process. Converting measured signals into cross-coupling components for determination of a complete coupling matrix C has been described.
WO 2011129828 A1 discusses various embodiments that include apparatus and methods of processing and geosteering with respect to well logging. Methods and associated apparatus can include acquiring signals generated from operating a tool rotating in a borehole of a well, where the tool includes a receiver antenna tilted with respect to the longitudinal axis of the tool and two transmitter antennas. The acquired signals can be processed with respect to a direction in the rotation of the tool to determine properties associated with a formation and/or to determine a geosignal for geosteering a drilling operation. WO 2011129828 A1 includes discussion of converting acquired signals to coupling components.
WO 2012030327 discusses various embodiments that include apparatus and methods of operation with respect to well logging. Apparatus and methods include a tool having an arrangement of transmitters and receivers that are operated at different positions downhole and a processing unit to process collected signals such that the arrangement of transmitters and receivers provides measurements that mimic operation of a different arrangement of transmitters and receivers.
WO 2012030327 discusses various embodiments that include apparatus and methods of operation with respect to well logging. Apparatus and methods include a tool having an arrangement of transmitters and receivers that are operated at different positions downhole and a processing unit to process collected signals such that the arrangement of transmitters and receivers provides measurements that mimic operation of a different arrangement of transmitters and receivers.
WO 2008076130 discusses electromagnetic resistivity logging systems and methods that employ an antenna configuration having at most two transmitter or receiver antenna orientations that rotate relative to the borehole. The measurements made by this reduced-complexity antenna configuration enable the determination of at least seven components of a coupling matrix, which may be determined using a linear system of equations that express the azimuthal dependence of the measurements. For increased reliability, averaging may be performed in azimuthally spaced and binned measurements. The coupling matrix components can then be used as the basis for determining logs of various formation parameters, including horizontal resistivity, vertical resistivity, and ratio of vertical resistivity to horizontal resistivity. The ratio of vertical resistivity to horizontal resistivity is a quantitative measure of anisotropy, and it can be replaced by the word anisotropy for simplicity in the discussions that follow.
In a formation model consisting of multiple thin layers, shoulder-bed effects occur and they have different influences on different coupling components. With respect to an induction measurement, a shoulder-bed effect (or a shoulder effect) is the influence on the induction measurement of a layer of interest by the adjacent layer above or below the layer being measured. Such effective coupling components cause inaccuracy in 0D inversion results. For example, at higher drilling wellbore inclination, the ZZ coupling component is affected more by shoulder-bed effects than one of the XX or the YY coupling components. Oppositely at lower drilling dip, such shoulder-bed effects dominate XX and YY coupling components. Consequently, 0D inversion utilizing these coupling components becomes problematic in thin-layer media.